1.) What would happen if these two questions on a recent test of mine were reversed (that is, #4 was given as #5 and #5 was given as #4)?
Sam Alexander essentially got this one right in that students would be more likely to apply a difference of cubes to problem #4. The students would likely pull out a 6x to get and claim the cube root of 4 is 2. As the problem is originally written, the more common issue is to attempt difference of squares instead. It’s possible to do the factoring with difference of cubes if one does not insist the factors are rational (use ) but the flat-out mistake is more likely.
2.) The following is a multiple choice question with the image removed. If a student were to ignore the math content of the answers (that is, guess), which would be the most common answer?
The conic section depicted can be categorized as:
This answer is nearly creepy, but the sort of thing that happens with priming all the time. Note the strong iteration of a single letter.
The Conic seCtion depiCted Can be Categorized as:
Hence the most likely choice by randomness would be C.
EDIT: As adroitly pointed out in the comments the word “cone” is also suggested by the setup word “conic”.
Once you’re aware of priming you will start to notice its effect more often. I stay on the lookout for situations where a student gets a problem wrong not because they didn’t know the mathematics but because they were influenced by the priming in surrounding problems.